Signals, Systems and Inference - Alan V. Oppenheim

【实例简介】
This book requires a strong foundation in signals and systems (see Oppenheim's classic Signals and Systems text, which is used in MIT's 6.003 course) as well as probability (see Bertsekas and Tsitsiklis's text, Introduction to Probability, used for MIT's 6.041 course).
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This publication is protected by Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions department. 221 River Street, Hoboken, NJ07030 10987654321 Library of Congress Cataloging-in-Publication Data Oppenheim, Alan V, 1937 Signals, systems and inference /Alan V Oppenheim and George C. Verghese Massachusetts Institute of Technology pag ISBN978-0-13-394328-3-ISBN0-13-3943283 1. Signal processing. I Verghese, George C II. Title TK5102.906732016 621.3822-dc23 2014043376 PEARSON 工SBN-13:978-0-13-394328-3 工SBN-10:0 394328 We dedicate this book to Amar bose. Bernard Gold and Thomas stockham George Sr and Mary Verghese, and Thomas Kailath These extraordinary people have had a profound impact on our lives and our careers This page intentionally left blank C ONTENTS reface The cover Acknowledgments Prologue XXIII 1 Signals and Systems 1 Signals, Systems, Models, and Properties 1.1.1 System Properties 1.2 Linear, Time-Invariant Systems 1.2.2 Eigenfunction and Transform Representation 1.2.1 Impulse-Response Representation of LTI System 13556 LTI SyStems 1.2.3 Fourier transforms 10 1.3 Deterministic Signals and Their Fourier Transforms ...... 11 1.3.1 Signal Classes and Their Fourier Transforms 1.3.2 Parsevals Identity, Energy Spectral Density, and Deterministic autocorrelation 14 1.4 Bilateral Laplace and z-Transforms 16 1.4.1 The Bilateral z-Transform 16 1.4.2 The Bilateral Laplace Transform 1.5 Discrete-Time Processing of Continuous-Time Signals 21 1.5.1 Basic Structure for DT Processing of CT Signals 22 1.5.2 DT Filtering and overall ct response ,,.24 1.5.3 Nonideal d/c converters 26 1.6 Further Reading 28 Problems Basic problems 29 Advanced Problems 40 Extension problems 51 Contents 2 Amplitude, Phase, and Group Delay 62 2.1 Fourier Transform Magnitude and Phase 62 2.2 Group Delay and the Effect of Nonlinear Phase 2.2.1 Narrowband Input signals 2.2.2 Broadband Input signals 68 2.3 All-Pass and Minimum-Phase Systems 73 2.3.1 All-Pass Systems 73 3.2 Minimum-Phase Systems 75 2.4 Spectral factorization 78 2.5 Further Reading 80 Problems 80 Basic problems 80 advanced Problems 88 Extension problems 100 3 Pulse-Amplitude modulation 102 3.1 Baseband Pulse-Amplitude modulation 103 3.1.1 The Transmitted signal 103 3.1.2 The Received signal 105 3.1. 3 Frequency-Domain Characterizations 105 3.1. 4 Intersymbol Interference at the Receiver .108 3.2N t pulses 3.3 Passband Pulse-Amplitude Modulation 113 3.3.1 Frequency-Shift Keying(FSK) .114 3.3.2 Phase-Shift Keying(PSK) 114 3.3.3 Quadrature-Amplitude Modulation(QAM) 116 3.4 Further Reading 118 Problems 119 Basic problems 119 advanced problems 123 Extension problems 126 4 State-Space Models 133 4.1 System memory 133 4.2 Illustrative Examples 134 4.3 State-Space Models ,,146 4.3.1 DT State-Space Models 146 4.3.2 CT State-Space Models .149 4.3.3 Defining Properties of State-Space Models 4.4 State-Space Models from LTI Input-Output Models 153 4.5 Equilibria and linearization of Nonlinear State-Space Models 158 4.5.1 Equilibrium 158 4.5.2 Linearization 161 Contents 4.6 Further Reading 164 Problems ,165 Basic problems 165 Advanced Problems Extension problems .172 5 LTI State-Space Models 174 1 Continuous-Time and Discrete- Time Lti models 174 5.2 Zero-Input Response and Modal representation 177 5.2.1 Undriven CT Systems 177 5.2.2 Undriven DT Systems 185 5.2.3 Asymptotic Stability of LTI Systems 187 5.3 General Response in Modal coordinates .,...191 5.3.1 Driven CT Systems 191 5.3.2 Driven DT Systems 194 5.3.3 Similarity Transformations and Diagonalizat 196 5. 4 Transfer Functions, Hidden Modes, Reachability, and observability 5.4.1 Input-State-Output Structure of cT Systems 202 5.4.2 Input-State-Output Structure of dT systems 210 5.5 Further Reading 219 Problems ..,220 Basic problems 220 advanced problems 228 Extension problems ..233 6 State observers and State Feedback 236 6.1 Plant and mo 237 6.2 State Estimation and observers 239 6.2.1 Real-Time simulation 239 6.2.2 The State observer ,,241 6. 2.3 Observer Design 243 6.3 State Feedback Control 252 6.3.1 Open-Loop Contro 252 6.3.2 Closed-Loop Control via LTi State Feedback 253 6.3.3 LTI State Feedback Design 254 6.4 Observer-Based Feedback Control 262 6.5 Further Reading 267 Problems 267 Basic problems 267 Advanced Problems 274 Extension problems 277 7 Probabilistic models 270 7.1 The Basic Probability mode 279 7.2 Conditional Probability, Bayes Rule, and Independence 280 Contents 7. 3 Random variables 283 7. 4 Probability distributions 283 7.5 Jointly Distributed Random variables 285 7.6 Expectations, Moments, and variance 287 7. 7 Correlation and Covariance for Bivariate random Variables 290 7.8 A Vector-Space Interpretation of Correlation Properties 294 7. 9 Further readins 296 Problems .297 Basic problems 297 advanced Problems 298 Extension problems .302 8 Estimation 306 8. 1 Estimation of a continuous random variable 307 8.2 From estimates to the estimator 312 8.2.1 Orthogonality .317 8.3 Linear Minimum Mean Square Error estimation 318 8.3.1 Linear estimation of one random variable from a Single measurement of Another 318 8.3.2 Multiple measurements 323 8.4 Further readin g 327 Problems 328 Basic problems 328 advanced Problems 332 Extension problems 338 9 Hypothesis Testing 343 9.1 Binary Pulse-Amplitude Modulation in Noise 343 9.2 Hypothesis testing with minimum Error probability .345 9.2.1 Deciding with Minimum Conditional Probability of error 346 9.2.2 MAP Decision Rule for Minimum Overall Probability of error 347 9.2.3 Hypothesis Testing in Coded Digital Communication .,350 9.3 Binary Hypothesis Testing 353 9.3.1 False alarm. Miss and detection ........... 354 9.3.2 The Likelihood Ratio Test .356 9.3.3 Neyman-Pearson Decision Rule and receiver Operating Characteristic .357 9.4 Minimum risk decisions 361 9. 5 Further reading 363 Problems 363 Basic problems 363 advanced Problems 368 Extension problems ..373 Contents 10 Random processes 380 10.1 Definition and Examples of a Random Process 380 10.2 First- and Second-Moment characterization of random Processes 385 10.3 Stationarity .386 10.3.1 Strict-Sense Stationarity 386 10.3.2 Wide-Sense Stationarity 386 10.3.3 Some Properties of wss Correlation and Covariance Functions 388 10.4 Ergodicity 391 10.5 Linear estimation of random processes 392 10.5.1 Linear prediction ..,392 10.5.2 Linear FIR Filtering 394 10.6 LTI Filtering of Wss Processes 395 10.7 Further Reading 401 Problems .401 Basic problem 401 Advanced Problems 406 Extension problems 412 11 Power Spectral Density 421 11.1 Spectral Distribution of Expected Instantaneous Power 422 11.1.1P 422 11.1.2 Fluctuation Spectral Density 426 11.1.3 Cross-Spectral Densit 431 11.2 Expected Time-Averaged Power Spectrum and the Einstein-Wiener-Khinchin Theorem .432 11.3 Applications 437 11.3.1 Revealing cyclic Components 437 11.3.2 Modeling Filters 439 11.3.3 Whitening Filters 443 11.3.4 Sampling Bandlimited Random Processes 444 11. 4 Further reading 444 Problems 445 Basic problems 445 advanced Problems 451 Extension problems 455 12 Signal Estimation 464 12.1 LMMSE EStimation for random variables 465 12.2 FIR Wiener filters 467 12.5 Optimal Observers and Kalman Filtering 12. 3 The Unconstrained dt Wiener filter 472 12. 4 Causal DT Wiener Filtering 480 487 12.5. 1 Causal Wiener Filtering of a Signal Corrupted by Additive noise 487 【实例截图】
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